Question

A sum of ₹ 2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of 1^st, 2^nd and 3^rd year. Do these interests form an A.P.? If so, find the interest at the end of the 27^th year.

Answer 1

Given: Principal P = 2000, Rate R = 7% per annum (simple interest).

Step-wise calculation:

1. Simple interest formula:

`SI = (P xx R xx T)/100`

2. Interest at end of 1^st year (T = 1):

`I_1 = (2000 xx 7 xx 1)/100` 

= 140

3. Interest at end of 2^nd year (T = 2):

`I_2 = (2000 xx 7 xx 2)/100`

= 280

4. Interest at end of 3^rd year (T = 3):

`I_3 = (2000 xx 7 xx 3)/100`

= 420

5. The sequence of interests is 140, 280, 420, ... . This is an A.P. with first term a = 140 and common difference d = 140.

6. Interest at end of 27^th year (a₂₇ = a + (27 – 1)d): 

a₂₇ = 140 + 26 × 140

= 140 × 27

= 3780

Interests at the end of 1^st, 2^nd and 3^rd years are 140, 280 and 420 respectively.

Yes, they form an A.P. (a = 140, d = 140).

Interest at the end of the 27^th year = 3780.